22 papers · ranked by Valyu relevance
Ilya Dumer, Kirill Shabunov
In this paper, we consider decoding algorithms that can achieve good performance and low complexity on moderate blocklengths. Our goal is to fill the void left by the best algorithms, such as optimum maximum likelihood (ML) decoding, which has unfeasible complexity even on relatively short blocks, and iterative…
Ilya Dumer, Kirill Shabunov
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding algorithms with nonexponential complexity known for RM codes. Decoding performance is…
Ilya Dumer
Successive cancellation (SC) decoding was considered in [1] for general Reed-Muller codes RM(r, m) of order r and dimension m. It was also proposed in [1] to set to zeros those information bits that are the least protected in SC decoding. Simulation results of [1] show that the resulting subcodes with frozen bits…
Noam Presman, Simon Litsyn
Polar codes are recursive general concatenated codes. This property motivates a recursive formalization of the known decoding algorithms: Successive Cancellation, Successive Cancellation with Lists and Belief Propagation. Using such description allows an easy development of these algorithms for arbitrary polarizing…
Marzieh Hashemipour-Nazari, Kees Goossens, Alexios Balatsoukas‐Stimming
'Alexios Balatsoukas‐Stimming'] Abstract—The recently introduced recursive projection aggregation (RPA) decoding method for Reed-Muller (RM) codes can achieve near-maximum likelihood (ML) decoding performance. However, its high computational complexity makes its implementation challenging for time- and…
Nithin Nagaraj, Arun Somani
Error detection is a fundamental need in most computer networks and communication systems in order to combat the effect of noise. Error detection techniques have also been incorporated with lossless data compression algorithms for transmission across communication networks. In this paper, we propose to incorporate a…
S. M. Hossein Tabatabaei Yazdi, Yongbo Yuan, Jian Ma, Huimin Zhao + 1 more
'Olgica Milenkovic'] We describe the first DNA-based storage architecture that enables random access to data blocks and rewriting of information stored at arbitrary locations within the blocks. The newly developed architecture overcomes drawbacks of existing read-only methods that require decoding the whole file in…
Adriano R. Lameira, Madeleine E. Hardus, Andrea Ravignani, Teresa Raimondi + 1 more
Recursive procedures that allow placing a vocal signal inside another of similar kind provide a neuro-computational blueprint for syntax and phonology in spoken language and human song. There are, however, no known vocal patterns among nonhuman primates arranged in self-embedded combinations that evince vocal recursion…
Yuan Li, Ying Guo, Osamu Hirota
Motivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs). Stabilizer quantum codes (SQCs) can be obtained by the different rows of the yielded circulant permutation matrices; hence, the quantum…
Sukhamoy Pattanayak, Abhay Kumar Singh, Pratyush Kumar
In this paper, we mainly study the some structure of cyclic DNA codes of odd length over the ring R = F 2 [u, v ] / h u 2 − 1, v 3 − v, uv − vu i which play an important role in DNA computing. We established a direct link between the element of ring R and 64 codons by introducing a Gray map from R to R 1 = F 2 + u F 2…
Julie D. Thompson, Raymond Ripp, Claudine Mayer, Olivier Poch + 1 more
The X circular code is a set of 20 trinucleotides (codons) that has been identified in the protein-coding genes of most organisms (bacteria, archaea, eukaryotes, plasmids, viruses). It has been shown previously that the X circular code has the important mathematical property of being an error-correcting code. Thus…
Sukhamoy Pattanayak, Abhay Kumar Singh
In this paper, we study the theory for constructing DNA cyclic codes of odd length over Z4[u]/hu2i which play an important role in DNA computing. Cyclic codes of odd length over Z4+uZ4 satisfy the reverse constraint and the reverse-complement constraint are studied in this paper. The structure and existence of such…
Sheri M. Markose, William B. Sherwin
This paper gives formal foundations and evidence from gene science in the post Barbara McClintock era that the Gödel Sentence, far from being an esoteric construction in mathematical logic, is ubiquitous in genomic intelligence that evolved with multi-cellular life. Conditions uniquely found in the Adaptive Immune…
Gerardo L. Febres, Boris Ryabko
This document introduces methods for describing long texts as groups of repeating symbols or patterns. The process converts a series of real-number values into texts. Developed tailored algorithms for identifying repeated sequences in the text are applied to decompose the text into nested tree-like structures of…
Kenny Daily, Paul Rigor, Scott Christley, Xiaohui Xie + 1 more
Background High-throughput sequencing (HTS) technologies play important roles in the life sciences by allowing the rapid parallel sequencing of very large numbers of relatively short nucleotide sequences, in applications ranging from genome sequencing and resequencing to digital microarrays and ChIP-Seq experiments. As…
Shubham Chandak, Joachim Neu, Kedar Tatwawadi, Jay Mardia + 7 more
As magnetization and semiconductor based storage technologies approach their limits, bio-molecules, such as DNA, have been identified as promising media for future storage systems, due to their high storage density (petabytes/gram) and long-term durability (thousands of years). Furthermore, nanopore DNA sequencing…
Ian Holmes
We describe a strategy for constructing codes for DNA-based information storage by serial composition of weighted finite-state transducers. The resulting state machines can integrate correction of substitution errors; synchronization by interleaving watermark and periodic marker signals; conversion from binary to…
Ian Holmes
We describe a strategy for constructing codes for DNA-based information storage by serial composition of weighted finite-state transducers. The resulting state machines can integrate correction of substitution errors; synchronization by interleaving watermark and periodic marker signals; conversion from binary to…
Authors not listed
Accurately modeling the dynamics of open quantum systems is critical for advancing quantum technologies, yet traditional methods often struggle with balancing accuracy and efficiency. Machine learning (ML) offers a promising alternative, particularly through recursive models that predict system evolution based on the…
Qi Zhang, Chang Liu, Stephen Wu, Ryo Yoshida
In the last few years, de novo molecular design using machine learning has made great technical progress but its practical deployment has not been as successful. This is mostly owing to the cost and technical difficulty of synthesizing such computationally designed molecules. To overcome such barriers, various methods…
Shubham Chandak, Kedar Tatwawadi, Billy Lau, Jay Mardia + 6 more
With the amount of data being stored increasing rapidly, there is significant interest in exploring alternative storage technologies. In this context, DNA-based storage systems can offer significantly higher storage densities (petabytes/gram) and durability (thousands of years) than current technologies. Specifically…
Lifu Song, Feng Geng, Ziyi Gong, Bingzhi Li + 1 more
High density and long-term features make DNA data storage a potential media. However, DNA data channel is a unique channel with unavoidable ‘data reputations’ in the forms of multiple error-rich strand copies. This multi-copy feature cannot be well harnessed by available codec systems optimized for single-copy media.…